The locus of midpoints of chords of the circle x²+y²=2r² subtending a right angle at the centre of the circle is

The centres of the circles are (a, c) and (b, c) and their radical axis is the y-axis. The radius of one of the circle is r. The radius of the other circle is

The tangents drawn from the origin to the circle x²+y²-2rx-2hy+h²=0 are perpendicular if

If x²+y²-2x+3y+k=0 and  x²+y²+8x-6y-7=0 cut each orthogonally, the value of k must be

The equation of the circle passing through the intersection of the circles x²+y²=2ax and x²+y²=2by and having its centre on the x/a-y/b=2 is

If O is the origin and OP, OQ are the tangents to the circles x²+y²+2gx+2fy+c=0 then the circumcentre of the ΔOPQ is

If a circle passes through the point (a, b) and cuts the circle x²+y²=k² orthogonally, the equation of the locus of its centre is

Let A be the centre of the circle x²+y²-2x-4y-20=0. Suppose that the tangent at the point B(1, 7) and D(4, -2) on the circle meet at the point C. The area of the quadrilateral ABCD is